from manim import *
class CustomCurve(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [25, 4, 0],
            [28,-12,0],
            [43,-15,0]
        ]
        self.set_points_smoothly(points)
class CustomCurve1(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [18, 4, 0],
            [22,-12,0],
            [43,-16,0]
        ]
        self.set_points_smoothly(points)

class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #镜头跟进效果 
        self.camera.frame.save_state()
         #题目出现
        text = Tex(r"\text{(张1000题10)求p的取值范围,使得}$\int ^{+\infty }_{1}\sin \dfrac{\pi }{x}\cdot \dfrac{dx}{\ln ^{p}x}$\text{收敛.}"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,20,0])
        
        self.play(Write(text))
        self.wait(0.1)
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)


        text5 = Tex(
                    r"\text{瑕点为}$+\infty $\text{和}$1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-35,0,0])
        self.play(Write(text5))
        text6 = Tex(
                    r"\text{当}$x\rightarrow +\infty $",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,-5,0])
        self.play(Write(text6))
        text7 = Tex(
                    r"$\sin \dfrac{\pi }{x}\cdot \dfrac{dx}{\ln ^{p}x}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-25,-5,0])
        self.play(Write(text7))
        text8 = Tex(
                    r"\text{等价于}$\dfrac{\pi }{x\ln ^{p}x}$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-5,0])
        self.play(Write(text8))


        text9 = Tex(
                    r"$\int _{2}^{+\infty }\dfrac{1}{x\ln ^{p}x}dx$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(Write(text9))
        text10 = Tex(
                    r"$\int _{2}^{+\infty }\dfrac{1}{\ln ^{p}x}d\ln x$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        text11 = Tex(
                    r"$\int _{\ln 2}^{+\infty }\dfrac{1}{t^{p}}dt$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(
            ReplacementTransform(text9,text10)
        )
        self.wait(0.5)
        self.play(
            ReplacementTransform(text10,text11)
        )
        self.wait(0.5)
        text12 = Tex(
                    r"\text{p>1时(收敛)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-15,0])
        self.play(Write(text12))
        text13 = Tex(
                    r"\text{p>1}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,12,0])
        self.play(Write(text13))
        self.play(
                  Uncreate(text12),Uncreate(text11)
                  )
        
        self.wait(0.2)


        text6 = Tex(
                    r"\text{当}$x\rightarrow 1 $",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,-15,0])
        self.play(Write(text6))
        text7 = Tex(
                    r"$\sin \dfrac{\pi }{x}\cdot \dfrac{dx}{\ln ^{p}x}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-25,-15,0])
        self.play(Write(text7))
        text8 = Tex(
                    r"\text{等价于}$\dfrac{\pi }{\left( x-1\right) ^{p-1}}$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-5,-15,0])
        self.play(Write(text8))
        text9 = Tex(
                    r"\text{与}$\dfrac{1}{\left( x-1\right) ^{p-1}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([18,-15,0])
        self.play(Write(text9))
        text12 = Tex(
                    r"\text{p-1<1时(收敛)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,-15,0])
        self.play(Write(text12))
        text13 = Tex(
                    r"\text{p<2}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,8,0])
        self.play(Write(text13))
        self.wait(0.5)
        #箭头引出
        arrow = Arrow(start=[5,-5,0],end=[-5,-10,0], color=RED
                       , stroke_width=20, tip_length=1)
        self.play(Create(arrow))
        text14 = Tex(
                    r"$\sin \dfrac{\pi }{x}$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([25,8,0])
        self.play(Write(text14))
        text15 = Tex(
                    r"$\sin \left( \pi -\dfrac{\pi }{x}\right) $",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([25,8,0])
        text16 = Tex(
                    r"$\sin \left( \dfrac{\pi \left( x-1\right) }{x}\right) $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([25,8,0])
        
        text17 = Tex(
                    r"$\sin \Delta \sim\Delta ,\Delta \rightarrow 0$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([25,0,0])
        self.play(
            ReplacementTransform(text14,text15)
        )
        self.wait(0.5)
        self.play(
            ReplacementTransform(text15,text16)
        )
        self.wait(0.5)
        self.play(Write(text17))
        self.wait()